NOVEMBER 23rd., 2004
EURANDOM, Laplace Building TU/e, Green Lecture Room (LG 1.105)
Francois Baccelli, INRIA and
Mean-Field Interaction Models for Large TCP Networks
In the tail-drop link, persistent flow case, the mean-field limit can be described geometrically as a billiards in the Euclidean space. This billiards has as many dimensions as the number of flow classes and as many reflection facets as there are routers and links. For non-persistent flows with an on-off structure, TCP can induce a turbulence like phenomenon which translates into two possible stationary regimes for the mean-field limit.
The AQM-RED link case can also be investigated by such mean-field techniques and leads to transport-type PDEs. In the single link case, this allows one to determine in closed form the stationary distribution of the stationary throughputs obtained by the flows, both in the persistent and the on-off cases.
When aggregated, the traffic generated by these models exhibits TCP and network-induced fluctuations that might explain some of the statistical properties observed on real traces.
|MINI-COURSE ON "stochastic geometry and
wireless network modeling "
October 26, 2004
Signal-to-Interference-Ratio Cells of a Spatial Point Process
Define the signal-to-interference-ratio (SIR) cell of point X to be the region of the space where the power received from X is larger than some linear function of the interference. In this definition, the interference at some location of the space is the sum of the powers received by this location from all points other than X.
In this lecture we will analyze a few basis stochastic
geometry questions pertaining to such SIR cells, in the case where the marks
representing powers are independent, like the volume and the shape of the
typical cell or the properties of the coverage of the space by SIR cells. We
will also discuss the relationship between SIR cells and classical objects
of stochastic geometry like Voronoi tessellations, germ grain models and the
December 14, 2004 Percolation and Connectivity in Mobile Ad Hoc Networks
February 8, 2005 Cross layer Optimization in Mobile Ad Hoc Networks
March 29, 2005 A spatial Erlang Formula and its application to the loss probability in large CDMA networks
June 8, 2005 The Radial Spanning Tree
(Joint work with C. Bordenave)